observations recorded at equally spaced intervals, nag_running_median_smoother (g10cac) fits a smooth curve through the data using one of two smoothers. They are based on the use of running medians and averages to summarise the overlapping segments. The fit is called the smooth, the residuals the rough and they obey the following:

Data = Smooth + Rough

The two smoothers are :

1.	4253H, twice consisting of a running median of 4, then 2, then 5, then 3 followed by Hanning. Hanning is a running weighted average, the weights being 1/4, 1/2 and 1/4. The result of this smoothing is then reroughed by computing residuals, applying the same smoother to them and adding the result to the smooth of the first pass.
2.	3RSSH, twice consisting of a running median of 3, two splitting operations named S to improve the smooth sequence, each of which is followed by a running median of 3, and finally Hanning. The end points are dealt with using the method described by Velleman and Hoaglin (1981). The full smoother 3RSSH, twice is produced by reroughing as described above.

The compound smoother 4253H, twice is recommended. The smoother 3RSSH, twice is popular when calculating by hand as it requires simpler computations and is included for comparison purposes.

4

References

Tukey J W (1977) Exploratory Data Analysis Addison–Wesley

Velleman P F and Hoaglin D C (1981) Applications, Basics, and Computing of Exploratory Data Analysis Duxbury Press, Boston, MA

5

Arguments

1: $smoother$ – Nag_Smooth_TypeInput

On entry: smoother must specify the method to be used.

$smoother = Nag_4253H$: 4253H, twice is used.
$smoother = Nag_3RSSH$: 3RSSH, twice is used.

Constraint:

smoother = Nag_4253H

Nag_3RSSH

2: $n$ – IntegerInput

On entry: the number,

n

, of the observations.

Constraint:

n > 6

n \leq 6

then the sequence is not long enough to carry out smoothing.

3: $y [n]$ – const doubleInput

On entry: the sample observations.

4: $smooth [n]$ – doubleOutput

On exit: contains the smooth.

5: $rough [n]$ – doubleOutput

On exit: contains the rough.

6: $fail$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument smoother had an illegal value.
NE_INT_ARG_LE: On entry, $n = 〈value〉$ .
Constraint: $n > 6$ .

7

Accuracy

Not applicable.

8

Parallelism and Performance

nag_running_median_smoother (g10cac) is not threaded in any implementation.

9

Further Comments

9.1

Internal Changes

Internal changes have been made to this function as follows:

At Mark 25: nag_running_median_smoother (g10cac) is a smoothing function with two possible smoothing methods. The function was previously using the incorrect method (i.e., if you asked for method A you would get method B, and vice versa).

For details of all known issues which have been reported for the NAG Library please refer to the Known Issues list.

10

Example

The example program reads in a sequence of 49 data taken from Tukey (1977), above. Results are obtained using the two smoothing methods described.

NAG Library Function Document

nag_running_median_smoother (g10cac)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

9.1 Internal Changes

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1

Purpose

2

Specification

3

Description